Allen, that sounds like a defective switch in the column. If I remember my circuit correctly, the brake light power goes from the foot switch, up into the column, through the turn signal switch, then back out the column to the tail lights. Did you check the ground at the back of the truck? The harness should be grounded somewhere near the driver side rear of the frame. The wiring circuit could have a faulty ground to the right side.

Good thing about your problem is that vehicle inspection stations don't check to see if your blinkers work while the brakes are applied.